Solve the system of equations.
y= x2 - 6
y=-2x + 9

Answer:

Dividing the number of balloon animal per the time he takes to make them you get an average of how many animals per minute Fred the clown can make.20/15=1,3 animals per minuteSince 0,3 is not a complete animal, the correct answer would be "Fred the clown can make 1 animal in 1 minute

Answer: 15 : 20

               6 : 8

               45 : 60

Step-by-step explanation:

First, you have to divide both numbers by 15:

15//15 = 1

20/15 = 4/3

Now you know that Fred can create 4/3 animal balloons in 1 minute.

If he spent 6 minutes creating animal balloons, then he can create 6 times as many animal balloons:

4/3 x 6 = 8

Now that we figured out the first part, we need to figure out how many he can make in 45 minutes.

We can do this by doing the same thing as we did for the first part, except we multiply 4/3 by 45 minutes:

4/3 x 45 = 60

Now that we figured out both parts, we know that our final answer should be:

15 : 20

6 : 8

45 : 60

Hope this helped! <3

The vertices of the triangle are the points where any pair of lines intersect.

We start by setting up the system

[tex]\begin{cases}y=-x+2\\y=2x-1 \end{cases} \iff -x+2=2x-1 \iff 3x=3 \iff x=1[/tex]

Using one of the two equations we can derive the correspondent y value:

[tex]f(x)=-x+2 \implies f(1)=-1+2 = 1[/tex]

So, one vertex is (1, 1)

We choose the other two pairs of lines to find the other vertices:

[tex]\begin{cases}y=-x+2\\y=x-2 \end{cases} \iff -x+2=x-2 \iff x=2 \implies y = 0[/tex]

[tex]\begin{cases}y=x-2\\y=2x-1 \end{cases} \iff x-2=2x-1 \iff x=-1 \implies y=-3[/tex]

So, the three vertices are (1, 1), (2, 0), (-1, -3).

Answer:

(1, 1), (2, 0), and (-1, -3)

Step-by-step explanation:

I got right on the test.

Answer:

D.

Step-by-step explanation:

The y-intercept is where the graph crosses the y-axis.

It crosses the y-axis at (0,5).

The graph is of f(t)=5*2^t where t is the number of years and the value of f(t) is the value of that coin after t years.

So we have (0,5) is on the graph of f which means f(0)=5.

f(0)=5 means at t=0 years the value of the coin is $5.

As per the y-intercept of a function, when the coin was purchased, the value of it was $5.

"The y-intercepts are points where the graph of a function crosses or touches the y-axis of the Cartesian Plane. "

The given function is

[tex]f(t)=5(2^{t})[/tex]

As per the graph of the given function, it starts from the point (0, 5).

Hence, it cuts the y-axis at point (0, 5).

Therefore, at the time of purchasing the coin, the value of the coin was at $5.

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Answer:

A) 40

Step-by-step explanation:

The sum of the interior angles of a regular polygon is:

[tex](n - 2) \times 180[/tex]

For a hexagon, we put n=6

[tex](6 - 2) \times 180 = 4 \times 180 = 720[/tex]

Let x be the 6th interior angle, then

[tex]x + 110 + 120 + 90 + 140 + 125 = 720[/tex]

[tex]x + 585 = 720[/tex]

[tex]x = 720 - 585 = 135[/tex]

The largest interior angle is 140°

Therefore the least exterior angle will be:

[tex]180 - 140 = 40[/tex]

The correct choice is A

Answer:

8100

Step-by-step explanation:

Step-by-step explanation:

We want to find the length of the square's diagonal.  Since the square has right angles, we can use Pythagorean theorem.

c² = a² + b²

x² = 90² + 90²

x = 90√2

x ≈ 127.3 feet

Answer:

(1,-1)

That is the ordered pair where they cross.

Step-by-step explanation:

The solution of the system is where the pair of lines there cross at.

The intersection is in the fourth quadrant there so your guess should definitely be of the form (positive, negative).

Only one choice is that and it is B.

It really does look like they cross at (1,-1).

To describe how to get from the origin to the intersection, I would say you would need to travel right 1 unit and down 1 unit.

We can even plug in our pair into both equations and see if it works.

y=x-2

y=4x-5

So if we plug in (1,-1) and assuming it is a solution, then both equations will give us the same thing on both sides. Let's try it:

y=x-2

-1=1-2

-1=-1

That's the same thing on both sides.

y=4x-5

-1=4(1)-5

-1=4-5

-1=-1

Again that is the same thing on both sides.

(1,-1) is indeed our solution.

Both the graph and the verification told us that.

Answer:

1, -1

Step-by-step explanation:

A.P.E.X 2021

Answer:

h(x) = 7 * (9/7) ^x

Step-by-step explanation:

h(x) = a b^x

When x=0 h(x) = 7

7 = a * b^0

7 = a *1

7 =a

Rewriting the equation

h(x) = 7 b^x

Let x=1

9 = 7 * b^1

9 = 7 * b

Divide each side by 7

9/7 =7b/7

9/7 =b

h(x) = 7 * (9/7) ^x

Answer:

Step-by-step explanation:

Area of rectangle = x³-5x²+3x-15

Width of rectangle = x²+3

Length of rectangle= ?

We will apply the formula:

Area= length* width

Hence we know the area and width.

x³-5x²+3x-15/x²+3 = length

By dividing the terms we get (x-5).

Thus the correct option is x-5....

Answer:

2^ (-1)

1/2

Step-by-step explanation:

Add the exponents which have common bases.

3 + (-4) = -1

2^ (-1)

1 / 2

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Answer:

The simplified form of the provided expression is [tex]2^{-1}\ or\ \frac{1}{2}[/tex]

Step-by-step explanation:

Consider the provided expression:

[tex](2^3)(2^{-4})[/tex]

Use the product rule of exponent:

[tex]a^m \cdot a^n=a^{m+n}[/tex]

Now use the above formula to simplify the provided expression.

[tex](2^3)(2^{-4})=2^{3+(-4)}[/tex]

[tex](2^3)(2^{-4})=2^{3-4}[/tex]

[tex](2^3)(2^{-4})=2^{-1}[/tex]

Hence, the simplified form of the provided expression is [tex]2^{-1}\ or\ \frac{1}{2}[/tex]

Answer:

27.5 m/s

275 m

Step-by-step explanation:

99 km/hr × (1000 m / km) × (1 hr / 3600 s) = 27.5 m/s

Distance = rate × time

d = 27.5 m/s × 10 s

d = 275 m

Answer:  The required scale factor of the dilation is 4.  

Step-by-step explanation:  Given that the parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.

We are to find the scale factor of the dilation.

From the graph, we note that

JH = 2 units   and   J'H' = 8 units.

We know that

[tex]\textup{Scale factor of dilation}=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the correponding side of the original figure}}.[/tex]

Therefore, the scale factor of the given dilation is

[tex]S=\dfrac{J'H'}{JH}\\\\\\\Rightarrow S=\dfrac{8}{2}\\\\\Rightarrow S=4.[/tex]

Thus, the required scale factor of the dilation is 4.  

Answer:

4 on edge

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

If there is any cyclic quadrilateral, which is a quadrilateral inscribed inside a circle, there is one simple property that is

the opposite angles add upto 180.

Thus we can say

96 + c = 180

and

d + 100 = 180

Since we need d, we use 2nd equation:

d + 100 = 180

d = 180 - 100

d = 80

Answer:

C) m∠5 + m∠6 =180°

D) m∠2 + m∠3 = m∠6

E) m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

TRUST ME! JUST TOOK MY QUIZ ON E2020

The correct equations are:

m∠2 + m∠3 + m∠5 = 180°

m∠2 + m∠5 =  m∠4

m∠5 + m∠6 = 180°

m∠2 + m∠3 =  m∠6

Equation is an expression used to show the relationship between two or more numbers and variables.

From the diagram:

m∠2 + m∠3 + m∠5 = 180° (sum of angles in a triangle)

But:

m∠3 + m∠4 = 180° (angle in a straight line)  

m∠2 + m∠3 + m∠5 = m∠3 + m∠4

m∠2 + m∠5 =  m∠4

Also:

m∠5 + m∠6 = 180° (angle in a straight line)

But:

m∠2 + m∠3 + m∠5 = 180

m∠2 + m∠3 + m∠5 = m∠5 + m∠6

m∠2 + m∠3 =  m∠6

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Answer: x^2-6x-8

Step-by-step explanation:

Step 1 : Factor - x^3-11x^2+22x+40: (x-5)(x^2-6x-8)/(x-5)

Step 2 : Divide, which should give you x^2-6x-8

Since the example circle is not shown, I can not answer thoroughly, but I will try my best.

The equation of a circle: (x - h)² + (y - k)² = r², where (h,k) is the center and r is the radius of the circle.

This means that for the radius to be two units, the right side of the equation is 2² = 4. So either B or d can be right.

Depending on the center of the given circle, we could narrow down to our final answer. If the center is (4,5), B is right, and if (5,4) is the center, D is right.

Due to the fact the example circle isn't proven, I can't solution thoroughly, but I will attempt my exceptional.

The equation of a circle: (x - h)² + (y - okay)² = r²,

in which (h, ok) is in the middle and r is the radius of the circle.

this means that for the radius to be two devices, the proper facet of the equation is two² = four. So either B or d can be right.

depending on the centre of the given circle, we ought to narrow right down to our very last answer. If the centre is (4, five), B is right, and if (five, four) is in the middle, D is proper.

The equation for a circle is given by:

(x-h)2+(y-k)2 = a2

Where (h,k) is the centre and a is the radius of the circle.

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Answer:

x = - [tex]\frac{1}{2}[/tex], x = 3

Step-by-step explanation:

Given

2x² - 5x - 3 = 0 ← in standard form

Consider the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 2 × - 3 = - 6 and sum = - 5

The factors are - 6 and + 1

Use these factors to split the x- term

2x² - 6x + x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x - 3) + 1 (x - 3) = 0 ← factor out (x - 3) from each term

(x - 3)(2x + 1) = 0

Equate each factor to zero and solve for x

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

x - 3 = 0 ⇒ x = 3

Answer:

C

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x + 9 ← is in slope- intercept form

with slope m = - 4

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex], hence

y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line

To find c substitute (4, 5) into the partial equation

5 = 1 + c ⇒ c = 5 - 1 = 4

y = [tex]\frac{1}{4}[/tex] x + 4 ← equation of perpendicular line → C

Answer:

12 cans with 3 left over

Step-by-step explanation:

It's pretty simple.

You already know you have 3 left over so all you have to do is 315 divided by 26.

315 ÷ 26 ≈ 12.12 but since you already know you have 3 left over, the answer would be 12.

Answer:

12 cans per carton

Step-by-step explanation:

Subtract the remainder of cans to the total amount.

315 - 3 = 312

Divide by the number of cartons.

312 / 36 = 12 cans per carton

Best of Luck!

Answer:

$60

The equation is x(5(2))=s or x(10)=s when x = number of weeks

Step-by-step explanation:

For 6 weeks, all you have to do is plug in the 6 where the x is.

6(5(2)) = s

6(10) = s

60 = s

or

6(10) = s

60 = s

Answer:

-6 - (-8) = 2.

Your number line might have a bubble at 2. Or it may show movement 8 units to the right of -6. Whatever it is, you should end up at the value of 2.

Step-by-step explanation:

We don't see a number line, but I can still show how to solve.

-6 - (-8) is the same as doing negative six plus negative one times negative 8. Or in number terms it would look like:

-6 + (- 1(- 8))

In the order of operations -- PEMDAS -- we do parenthesis first.

- 1( - 8) = 8, so we simplify by plugging this value back into the equation:

-6 + 8

-6 + 8 is the same as 8 - 6.

8 - 6 = 2

Your answer is 2.

Answer:

The first graph represents how many of each order could be put in a bag hanging from the hook ⇒ 1st

Step-by-step explanation:

* Lets explain how to solve the problem

- The order of jumbo paperclips weighs 2 pounds

- x is the number of orders of paperclips

∴ The weight of the paperclips order is 2 × x = 2x

- The order of packing tape weighs 3 pounds

- y is the number of orders of packing  tape

∴ The weight of the tape order is 3 × y = 3y

- The weight of the total order is 2x + 3y

- The hook can hold no more than 6 pounds

∴ 2x + 3y ≤ 6

- Lets find the graph which represent this inequality

∵ The equation of any line is y = mx + c, where m is the slope of the

  line and c is the y-intercept

- The y-intercept means substitute x in the equation by 0

- The x- intercept means substitute y in the equation by 0

∵ The inequality is 2x - 3y ≤ 6

∵ The equation of the line is 2x + 3y = 6

- Subtract 2x from both sides

∴ 3y = 6 - 2x

- Divide both sides by 3

∴ y = 6/3 - 2/3 x

∴ y = 2 - 2/3 x

- Find the y-intercept

∵ x = 0

∴ y = 2

∴ The line intersect the y-axis at point (0 , 2)

- Find the x-intercept

∵ y = 0

∴ 0 = 2 - 2/3 x

- Add 2/3 x to both sides

∴ 2/3 x = 2

- Multiply both sides by 3

∴ 2 x = 6 ⇒ divide both sides by 2

∴ x = 3

∴ The line intersect the x-axis at point (3 , 0)

- From the figure the first and the second figures have the same

 x-intercept and y-intercept

∵ The inequality is 2x + 3y ≤ 6

- The sign ≤ means the line is sold and the shading is under the line

∴ The first figure is the answer

* The first graph represents how many of each order could be put in a

  bag hanging from the hook

Answer:

Option A.

Step-by-step explanation:

Let x is the number of orders of paperclips and y is the number of orders of packing tape.

An order of jumbo paperclips weighs 2 pounds and an order of packing tape weighs 3 pounds.

Total weight = [tex]2x+3y[/tex]

A hook in an office storage closet can hold no more than 6 pounds. It means total weight must be less than or equal to 6 pounds.

[tex]2x+3y\leq 6[/tex]

The related equation is

[tex]2x+3y=6[/tex]

Substitute x=0 in the above equation.

[tex]2(0)+3y=6[/tex]

[tex]3y=6[/tex]

[tex]y=2[/tex]

The y-intercept is 2.

Substitute y=0 in the above equation.

[tex]2x+3(0)=6[/tex]

[tex]2x=6[/tex]

[tex]x=3[/tex]

The x-intercept is 3.

Check the inequality by (0,0).

[tex]2(0)+3(0)\leq 6[/tex]

[tex]0\leq 6[/tex]

This statement is true, it means (0,0) is included in the shaded region.

The sign of inequity is "≤" it means the related line is a solid line and shaded region lie below the line.

Therefore, the correct option is A.

The probability that a player wins the game by adding the numbers from the slips drawn from the box is 40%. If the rule changes and the player multiplies the numbers instead of adding them, the winning probability increases to 70%.

The game consists of drawing two numbers from the box and verifying whether their sum or product is even or odd. In Mathematics, for the sum to be even, both numbers must be odd or both must be even. If we check, we have 2 odd numbers (7, 9) and 3 even numbers (4, 6, 8). The combinations for even sum could be odd-odd or even-even. The total successful events would be 1 (odd-odd) + 3 (even-even) = 4 out of total 10 possible events (5C2), which gives us the probability of the player winning the game as 4/10 or 40%

Now, whether the probability changes when we multiply instead of adding: Yes, it does! In Mathematics, an even number results when multiplying any number by an even number, regardless of whether the other number is odd or even. Therefore, since 3 out of 5 numbers are even, the probability that the player wins if they multiply the two numbers they select instead of adding them is greater, confirmed by calculating combinations again and we find 7 out of 10 possible events yield an even product, therefore probability is 70%, which is greater than that of adding them.

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[tex]\huge{\boxed{\text{3) \bf{9, 40, 41}}}}[/tex]

A Pythagorean triple is a set of three numbers where [tex]a^2 + b^2 = c^2[/tex].

Trying 1:

[tex]1^2+3^2=10^2[/tex]

[tex]1+9=100[/tex]

[tex]10=100[/tex]

Incorrect.

Trying 2:

[tex]4^2+5^2=9^2[/tex]

[tex]16+25=81[/tex]

[tex]41=81[/tex]

Incorrect.

Trying 3:

[tex]9^2+40^2=41^2[/tex]

[tex]81+1600=1681[/tex]

[tex]1681=1681[/tex]

Correct!

Trying 4: (unnecessary, but practice is good)

[tex]16^2+30^2=44^2[/tex]

[tex]256+900=1936[/tex]

[tex]1156=1936[/tex]

Incorrect.

Answer:

[tex]\large\boxed{f^{-1}(x)=9x-18}[/tex]

Step-by-step explanation:

[tex]f(x)=\dfrac{1}{9}x+2\to y=\dfrac{1}{9}x+2\\\\\text{exchange x to y and vice versa}\\\\x=\dfrac{1}{9}y+2\\\\\text{solve for y}\\\\\dfrac{1}{9}y+2=x\qquad\text{subtract 2 from both sides}\\\\\dfrac{1}{9}y=x-2\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{1}{9\!\!\!\!\diagup_1}y=9x-(9)(2)\\\\y=9x-18[/tex]

Answer:

-4 is the mimumum of y=-3+cos(x+4)

Step-by-step explanation:

The minimum value of y=cos(x) is -1.

The minimum value of y=cos(x+4) is still -1; the +4 inside the cosine function only affected the horizontal shift.

The minimum value of y=-3+cos(x+4) is -3-1 which is -4.  This brought the graph down 3 units so if the minimum was previously -1 and it got brought down 3 units then it's new minimum is -4.

the question is already in slope intercept form.

The y-intercept is 12.

y=mx+b whereas m=slope, and b=y-intercept.

hope this helped!

The function is linear function of a form,

[tex]f(x)=ax+b[/tex]

Which always intersects point,

[tex]P(x, n)[/tex]

Or in this case,

[tex]f(x)=2x+12[/tex]

The point is therefore,

[tex]P(x,y)\Longrightarrow\boxed{P(x, 12)}[/tex]

The y-intercept is 12.

Hope this helps.

r3t40

Answer:

C

Step-by-step explanation:

[tex] \sec( \alpha ) = \frac{1}{ \cos( \alpha ) } \\ \\ \sec( \alpha ) = \frac{1}{ \frac{ad}{hip} } \\ \\ \sec( \alpha ) = \frac{hip}{ad} \\ \\ \sec( \alpha ) = \frac{41}{40} [/tex]

The value of the secθ is 41/40.

Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.

For the given situation,

The diagram shows the right-angled triangle.

The sides of the right-angled triangle are

Hypotenuse side = 41 ft

Opposite side = 9 ft

Adjacent side = 40 ft

The value of secθ is

[tex]sec \theta =\frac{1}{cos \theta}[/tex]

where, [tex]cos \theta =\frac{adjacent}{hypotenuse}[/tex]

⇒ [tex]sec \theta =\frac{hypotenuse}{adjacent}[/tex]

⇒ [tex]sec \theta =\frac{41}{40}[/tex]

Hence we can conclude that the value of the secθ is 41/40.

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Answer:

Part A)

This quadratic expression can be factored by using the difference of squares pattern.

Part B) (5x+y) and (5x-y)

Step-by-step explanation:

Given:

25x^2-y^2

above polynomial can be factorize by using difference of squares formula

a2-b2=(a+b)(a-b)

25x^2-y^2= (5x-y)(5x+y)

so for part A)

correct option is  This quadratic expression can be factored by using the difference of squares pattern.

Part B)

As factored above in part A,

the factors of given polynomial 25x^2-y^2 are (5x+y)(5x-y)

so for part B) correct options are (5x+y) and (5x-y) !